Truncated tetrapentagonal tiling explained

In geometry, the truncated tetrapentagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of t_0,1,2 or tr.

Symmetry

There are four small index subgroup constructed from [5,4] by mirror removal and alternation. In these images fundamental domains are alternately colored black and white, and mirrors exist on the boundaries between colors.A radical subgroup is constructed [5*,4], index 10, as [5⁺,4], (5*2) with gyration points removed, becoming orbifold (

• 22222

), and its direct subgroup [5*,4]⁺, index 20, becomes orbifold (22222).

See also

• Uniform tilings in hyperbolic plane
• List of regular polytopes

References

• John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things 2008, (Chapter 19, The Hyperbolic Archimedean Tessellations)
• Book: Coxeter, H. S. M.. H. S. M. Coxeter

. H. S. M. Coxeter. The Beauty of Geometry: Twelve Essays. 1999. Dover Publications. 99035678. 0-486-40919-8. Chapter 10: Regular honeycombs in hyperbolic space.

External links

• • • Hyperbolic and Spherical Tiling Gallery
• KaleidoTile 3: Educational software to create spherical, planar and hyperbolic tilings
• Hyperbolic Planar Tessellations, Don Hatch